Theoretical analysis of vascular regulatory mechanisms contributing to retinal blood flow autoregulation

Abstract

Purpose: To study whether impaired retinal autoregulation is a risk factor for glaucoma, the relationship between vascular regulatory mechanisms and glaucoma progression needs to be investigated. In this study, a vascular wall mechanics model is used to predict the relative importance of regulatory mechanisms in achieving retinal autoregulation.

Methods: Resistance vessels are assumed to respond to changes in pressure, shear stress, carbon dioxide (CO2), and the downstream metabolic state communicated via conducted responses. Model parameters governing wall tension are fit to pressure and diameter data from porcine retinal arterioles. The autoregulation pressure range for control and elevated levels of IOP is predicted.

Results: The factor by which flow changes as the blood pressure exiting the central retinal artery is varied between 28 and 40 mm Hg is used to indicate the degree of autoregulation (1 indicates perfect autoregulation). In the presence of only the myogenic response mechanism, the factor is 2.06. In the presence of the myogenic and CO2 responses, the factor is 1.22. The combination of myogenic, shear, CO2, and metabolic responses yields the best autoregulation (factor of 1.10).

Conclusions: Model results are compared with flow and pressure data from multiple patient studies, and the combined effects of the metabolic and CO2 responses are predicted to be critical for achieving retinal autoregulation. When IOP is elevated, the model predicts a decrease in the autoregulation range toward low perfusion pressure, which is consistent with observations that glaucoma is associated with decreased perfusion pressure.

Keywords: autoregulation; blood flow regulation; glaucoma; metabolic response; myogenic response; retina.

Figure 1.

Representative segment model. The retinal vasculature is represented by five compartments downstream of the CRA and upstream of the central retinal vein (CRV). The blue dotted line indicates the compartments considered in this model. The vessels in the LA and SA compartments are assumed to be vasoactive, and the remaining compartments are fixed resistances.

Figure 2.

Parameter estimation for passive and active wall tension functions. (A) Diameter of small arterioles (D_SA) and (B) large arterioles (D_LA) as a function of arterial pressure. Model predicted values for passive diameters (thin curve) are compared with data from passive diameter responses (closed circles) in porcine retinal arterioles. (C) Diameter of small arterioles and (D) large arterioles as a function of arterial pressure. Model predicted values for the active response (thin curve) include myogenic and carbon dioxide mechanisms and are compared with data from active diameter responses (closed circles) in cat brain pial arterioles.

Figure 3.

(A) Comparison of model predicted velocity values (black squares) with experimental measures (black dots, open triangles, dashed line⁵²) for different-sized vessels. The solid line corresponds to the best fit line to the experimental data, as determined in a study by Riva et al. (B) Rate of blood flow (Q) as a function of vessel diameter for arterioles and venules. Solid curve is the power curve fit to the data points from arteries and veins (black dots). Riva et al. found that Q_A = 2e − 5D^2.76 and Q_V = 8.25e − 6D^2.84 where diameter is in micrometers. Additional measures of blood flow for different vessel sizes are included from Feke et al.⁵³ (plusses), Dumskyj et al. (open circles), Rassam et al. (asterisks), Garcia Jr et al. (open triangles), and Grunwald et al. (dashed line). Black squares correspond to model predicted flow values in the control state.

Figure 4.

(A) Decline of oxygen saturation along the vascular network (compartments are colored and labeled) for incoming pressures of P_a = 32 (low), 40 (medium), and 64 mm Hg (high). (B) Increase in carbon dioxide content of blood along the vascular network. Pressures as in (A).

Figure 5.

(A) Change in blood flow as pressure, P_a, is increased, providing a measure of the degree of blood flow autoregulation. P_a is defined as the pressure at the downstream end of the CRA. The dashed line represents a passive vessel response when no regulatory mechanisms are active. Individual and combined roles of myogenic, shear, conducted metabolic, and carbon dioxide mechanisms on autoregulation are evaluated at a control level of IOP = 15 mm Hg. (B) Corresponding changes in LA diameter with pressure. (C) Corresponding changes in SA diameter with pressure.

Figure 6.

Model predicted autoregulation curves for IOP = 15 mm Hg (control) and IOP = 25 mm Hg (elevated). (A) For IOP = 15 mm Hg, the model predicted autoregulation curve (solid curve) is plotted with clinical data obtained from Feke and Pasquale. (squares and triangles), Dumskyj et al. (circles), Feke et al. (diamonds), and Grunwald (stars). (B) Normalized flow plotted as a function of P_a for IOP = 15 mm Hg (blue) and IOP = 25 mm Hg (red). (C) Normalized flow plotted as a function of OPP_ret. Colors as in (B).